Equivalent Representations of Set Functions

References

  • Abramowitz M. , Stegun I. A. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (1970) (Dover Publications, New York) . 7th printing Google Scholar
  • Aumann R. J. , Shapley L. S. Values of Non-Atomic Games (1974) (Princeton University Press, Princeton, NJ) Google Scholar
  • Banzhaf J. F. Weighted voting doesn't work: A mathematical analysis. Rutgers Law Rev. (1965) 19 317 343 Google Scholar
  • Denneberg D. , Grabisch M. Interaction transform of set functions over a finite set. Inform. Sci. (1999) 121 1-2 149 170 CrossrefGoogle Scholar
  • Dubey P. , Shapley L. S. Mathematical properties of the Banzhaf power index. Math. Oper. Res. (1979) 4 99 131 LinkGoogle Scholar
  • Gilboa I. , Schmeidler D. Canonical representation of set functions. Math. Oper. Res. (1995) 20 197 212 LinkGoogle Scholar
  • Grabisch M. Alternative representations of discrete fuzzy measures for decision making. Internat. J. Uncertainty, Fuzziness, and Knowledge-Based Systems (1997) 5 587 607 CrossrefGoogle Scholar
  • Grabisch M. k-order additive discrete fuzzy measures and their representation. Fuzzy Sets and Systems (1997) 92 167 189 CrossrefGoogle Scholar
  • Grabisch M. , Roubens M. An axiomatic approach to the concept of interaction among players in cooperative games. Internat. J. Game Theory (1999) 28 547 565 CrossrefGoogle Scholar
  • Hammer P. L. , Holzman R. Approximation of pseudo-Boolean functions; Applications to game theory. ZOR—Methods and Models of Oper. Res. (1992) 36 3 21 CrossrefGoogle Scholar
  • Hammer P. L. , Rudeanu S. Boolean Methods in Operations Research and Related Areas (1968) (Springer, Berlin, Germany) CrossrefGoogle Scholar
  • Harsanyi J. C. A simplified bargaining model for the n-person cooperative game. Internat. Econom. Rev. (1963) 4 194 220 CrossrefGoogle Scholar
  • Lovász L. , Bachem A. , Grötschel M. , Korte B. Submodular function and convexity. Mathematical Programming. The State of the Art. Bonn 1982 (1983) (Springer-Verlag, Berlin-Heidelberg-New York-Tokyo) 235 257 CrossrefGoogle Scholar
  • Marinacci M. Decomposition and representation of coalitional games. Math. Oper. Res. (1996) 21 1000 1015 LinkGoogle Scholar
  • Murofushi T. , Soneda S. Techniques for reading fuzzy measures (III): Interaction index. 9th Fuzzy System Sympos. (1993) Sapporo, Japan (In Japanese.) 693 696 Google Scholar
  • Owen G. Multilinear extensions of games. Management Sci. (1972) 18 64 79 LinkGoogle Scholar
  • Owen G. , Roth A. E. Multilinear extensions of games. The Shapley Value. Essays in Honor of Lloyd S. Shapley (1988) (Cambridge University Press, Cambridge, UK) 139 151 CrossrefGoogle Scholar
  • Pap E. Null-additive set functions (1995) (Kluwer Academic, Dordrecht, The Netherlands) Google Scholar
  • Rota G. C. On the foundations of combinatorial theory I. Theory of Möbius functions. Z. Wahrscheinlichkeitstheorie und Verwandte Gebiete (1964) 2 340 368 CrossrefGoogle Scholar
  • Roubens M. Interaction between criteria and definition of weights in MCDA problems. (1996) 44th Meeting of the European Working Group “Multicriteria Aid for Decisions” Brussels, Belgium Google Scholar
  • Shafer G. A Mathematical Theory of Evidence (1976) (Princeton University Press, Princeton, NJ) CrossrefGoogle Scholar
  • Shapley L. S. , Kuhn H. W. , Tucker A. W. A value for n-person games. Contributions to the Theory of Games (1953) II (Princeton University Press, Princeton, NJ) 307 317 . Ann. Math. Stud. 28 CrossrefGoogle Scholar
  • Singer I. Extensions of functions of 0–1 variables and applications to combinatorial optimization. Numer. Funct. Anal. Optim. (1984-85) 7 23 62 CrossrefGoogle Scholar
  • Weber R. J. , Roth A. E. Probabilistic values for games. The Shapley Value. Essays in Honor of Lloyd S. Shapley (1988) (Cambridge University Press, Cambridge, UK) 101 119 CrossrefGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.